Occupation detection using Face API
In short, it's possible to achieve occupation detection via face but it's highly doubtful that it can be done with Face API that you mentioned.

Now some details,

Face preception is a very complex job. You have so many parameters to consider before even beginning to design the model. 


  Many different types of important information are visible in faces and
  the processes and mechanisms involved in extracting this information
  are complex and can be highly specialized.


and 


  Face perception serves as the basis for much of human social exchange.
  Diverse information can be extracted about an individual from a single
  glance at their face, including their identity, emotional state, and
  direction of attention.


Extracting that much information is not easy. 

Face API:

Face API gives you 


Face Similarity (checks how similar two or more faces are)
Face Identification (gives you 27 landmarks like age, gender, facial hair, smile etc confidence level)
Emotion detection (check what kind of emotion the face has)


However, in my view, occupation detection via face will going to need a lot more than these basic parameters.

However, previous work utilizing single person’s nearly frontal clothing information and fore/background context preliminarily proves that occupation recognition is computationally feasible in computer vision. 

However, in practice, multiple people with arbitrary poses are common in a photo, and recognizing their occupations is even more challenging. 

You have to appropriately built visual attributes, co-occurrence, and spatial configuration model that is learned through structure SVM or deep neural nets to recognize multiple people’s occupations in a photo simultaneously.

I am attaching some research papers so you can review them to get more insight.

Reference Papers:

A Comparative View of Face Perception

The many faces of research on face perception

What Do You Do? Occupation Recognition in a Photo via Social Context

Note: 

Please state your question clearly (like: tell us your problem in detail, and your approach to solve it), and also tell what research you have done before asking the question. Please see how much research effort is expected of stackoverflow users before they post any new questions.